Very Large Cliques are Easy to Detect

Andreev, Alexander E.; Jukna, Stasys

doi:10.4230/DagSemProc.06111.22

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Very Large Cliques are Easy to Detect

Authors Alexander E. Andreev, Stasys Jukna

Part of: Volume: Dagstuhl Seminar Proceedings, Volume 6111
Part of: Series: Dagstuhl Seminar Proceedings (DagSemProc)
License: Creative Commons Attribution 4.0 International license
Publication Date: 2006-11-20

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DOI: 10.4230/DagSemProc.06111.22
URN: urn:nbn:de:0030-drops-6092

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Keywords

Clique function
monotone circuits
perfect hashing

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Abstract

It is known that, for every constant $kgeq 3$, the presence of a
  $k$-clique (a complete subgraph on $k$ vertices) in an $n$-vertex
  graph cannot be detected by a monotone boolean circuit using fewer
  than $Omega((n/log n)^k)$ gates.  We show that, for every constant
  $k$, the presence of an $(n-k)$-clique in an $n$-vertex graph can be
  detected by a monotone circuit using only $O(n^2log n)$ gates.
  Moreover, if we allow unbounded fanin, then $O(log n)$ gates are
  enough.

Cite As Get BibTex

Alexander E. Andreev and Stasys Jukna. Very Large Cliques are Easy to Detect. In Complexity of Boolean Functions. Dagstuhl Seminar Proceedings, Volume 6111, pp. 1-7, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006) https://doi.org/10.4230/DagSemProc.06111.22

Author Details

Alexander E. Andreev

Stasys Jukna

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